This uncertainty representation is generally valid for small perturbations that are added to a given pose \(\hat{{\mathbf {T}}} = {\mathbf {T}}\mathrm {exp}({\mathbf {\xi }})\)  where \({\mathbf {\xi }}\sim \mathcal {N}(\mathbf {0}, {\mathbf {\Sigma }})\)[1]}.
The equation above matches the error definition in Eq. REF , that is \({\mathbf {\xi }}\in \mathbb {R}^6\)  can be viewed as the error between the real transformation and its estimate.
